Dear Dr. Debbie,
Our second grader struggled so much with math this year that his teacher suggested we invest in workbooks this summer. She mentioned concepts such as number line, patterns, and categorization that need to be worked on. The whole family was really looking forward to a break from school, so I’m wondering if there aren’t some more exciting activities than workbooks for sharpening his math skills.
School’s Out for Summer
Don’t miss last week’s column Band Aids for Nonexistent Boo Boos — Good Parenting
Dear S.O. S.,
Basic math skills are best learned through hands-on experience, not worksheets. Over sixty years ago, Jean Piaget gave us a framework by which early childhood educators plan “age appropriate” activities. He believed that learning and problem solving are different at each stage of development and that early experiences provide a foundation for taking in new information as the child matures. Before your son can move on successfully with math skills, he needs to master the earlier stages.
SENSORI-MOTOR, ages 0 to 2 years
This is the age of physical exploration of the world. It’s never too late for your son to enjoy sensory play and to use more than one sense for comparisons, classification, counting and measuring.
Scoop sand or water – at the beach, of course! with various size containers to make comparisons of volume and weight. Listen to birdcalls outside and match the sounds to the type of bird. A field guide (book) or the internet can help with this. Make and compare summertime smoothies and juicicles with different ingredients. Collect and count up rocks or shells and compare or classify them by touch. Count the seconds between a lightening flash and a thunder boom during a summer thunderstorm.
SYMBOLIC THINKING, 2 to 7 years
In the next phase of development, language skills blossom which supports lots of imaginative play and symbolic thinking. Now he has words at his disposal that can stand for objects, actions, and emotions. At this stage he should be doing more thinking as he plays, rather than just doing. Your comments and conversation as he plays enrich his vocabulary and help to fine tune his grammar and he puts his ideas into words with your help. And incidentally, language is necessary for the symbolism used in mathematics.
Colors, shapes, and sizes are mathematical constructs and have their own words. Use them often. With these words, you can help your son find and make patterns during daily activities. Serve him pancakes in two shapes or two sizes and lead him to lay them, big-little-big-little, or square-circle-square-circle, around his breakfast plate. Make fruit kabobs on wooden skewers with melon balls, berries, and other fruits of different colors. Layer a lunch sandwich with slices of cheese-tomato-cheese-tomato. Look for repeating patterns in nature, architecture, clothing, etc. on your excursions. Let him use a camera to capture a row of rectangles on a city block or a shimmer of concentric circles on a spider web in your yard. Give him art supplies to dabble in his own pattern-making.
The concept of a number line is key for addition, subtraction, and more complex operations to come. Beyond understanding none and all, more and less, your son needs to be able to work with specific quantities. Turn a staircase into a number line by attaching numerals in ascending order. A “higher” number makes sense now. Try painter’s tape for a smooth surface, and felt or Velcro strips for carpet. Call out the numbers for him – forward or backwards as he goes up or down – until you hear him doing it himself. Then challenge him to climb two steps at a time – calling out the numbers as he goes. Next, coax him to scale up four steps from the bottom, then two more to see what number that is. If your home has no stairs, or fewer than ten, consider chalking a sidewalk with evenly spaced numerals or taping numerals on a floor. Make up a simple version of hopscotch or roll a ball or toy truck across the line so your son can play with the idea of numbers being in order from smaller to larger before having him do actual addition and subtraction on his step-size number line.
Pretend play is an excellent activity for lots of learning. Pretend play is still age appropriate for a rising third grader, particularly one who doesn’t yet grasp some math essentials. Toy vehicles, animals, and people, as well as any kind of construction set (wood blocks, Legos, etc.) encourage the use of symbolic thinking since these objects are used to represent real or imagined actions. Dress up clothes and household props, which can include the very versatile bath towel (cape, cloak, apron, baby doll blanket, magic carpet, etc.), similarly invite imagination. Blocks, as well as other pretend play, also offer an opportunity for you to reinforce words about spatial relationships – over, under, beside, between, around, through, which will be essential for working with geometry in a few years.
Board games and card games have a lot of math built in to them. Choose one or two to play regularly as a family this summer. Dominoes and dice will teach your son the visual patterns that make up three dots, or five dots, or six dots. Recognizing a quantity without stopping to count is a math skill called “subatizing.” For some games, each player gets a playing piece. This is a math concept known as “one-to-one correspondence.” If there is paper money involved in a game, your son gets practice in adding up ones, fives, tens, etc. as his fortune grows. A game with a score sheet can be used to teach him how to use tally marks – an ancient method of adding up by fives.
CONCRETE OPERATIONS, 7 to 11 years
The expectation for the next stage of mathematical thinking is that your son will no longer need to be walking out the actual distance on a number line, nor to manipulate actual objects for adding and subtracting. This next period is when he will be able to use nothing more than a pencil to solve a problem on a worksheet. I suspect he’s not quite there yet.
For a more solid foundation for his next year at school, skip the workbooks and enjoy some real mathematical fun together.
Dr. Debbie
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What do you think? Email your comments or questions to Dr. Debbie at editor[at]chesapeakefamily.com.
